Shortly after Scalia's death became public Saturday, Senate Republican leaders said they would not move forward on any nominee put forward by President Barack Obama. They received back-up from their Senate colleagues running for president on Sunday.

"Absolutely," Sen. Ted Cruz, R-Texas, said when asked on ABC's "This Week" if he would filibuster "anyone" nominated by Obama to replace Scalia. Asked the same question, Sen. Marco Rubio, R-Fla., said, "Yeah. But he won't have to," since it's unlikely that Majority Leader Mitch McConnell, R-Ky., will bring up a nominee on the floor.

But while Democrats can't schedule hearings or votes on a nominee, they have their own options. "It’s the majority that sets the agenda, but the minority who drives the agenda," Sen. Joe Manchin III, D-W.Va., said earlier this month . That is a reflection of the reality in the chamber. Even with Republicans in control of both chambers for this Congress, Democrats can block virtually anything they want from coming to the floor.

And that could disrupt the GOP's strategy to show that the Senate "is working again" by approving all of its appropriations bills in an orderly fashion this year.

Last year, for example, Democrats signaled they would block any appropriations bill that adhered to the automatic, across-the-board spending cuts known as sequestration. Despite repeated attempts by Republicans to bring up spending bills, Democrats moved to impede their progress to the floor, holding out until they got a budget deal they could live with in October, That paved the way for a year-end omnibus spending package in December that lifted those spending restrictions.

Since returning to the majority in January 2015, Senate Republicans have stressed they are committed to making the institution work.

"We're going to continue to work here as Republicans in the Senate on the issues that we think are important to the American people and good for America's national security and economic security interests,” was how Senate Republican Conference Chairman John Thune, R-S.D., put it on Feb. 9 at the GOP’s weekly press conference.

Democrats have been equally on message that the only reason the Senate might be working now is that they are a "constructive minority," in the words of Senate Minority Leader Harry Reid, D-Nev., unlike their GOP counterparts when they were out of power.

Obama said Sunday that he does not plan to submit a nominee until the Senate returns from this week's recess, But Republicans are adamant that the president shouldn't submit a nominee at all. They say tradition dictates that presidents don't get to appoint Supreme Court justices in the final year of their term.

“The fact of the matter is that it’s been standard practice over the last nearly 80 years that Supreme Court nominees are not nominated and confirmed during a presidential election year," Senate Judiciary Chairman Charles E. Grassley, R-Iowa, said in a statement Saturday evening.

"Given the huge divide in the country, and the fact that this president, above all others, has made no bones about his goal to use the courts to circumvent Congress and push through his own agenda, it only makes sense that we defer to the American people who will elect a new president to select the next Supreme Court Justice.”

Cruz and Rubio, and other Republicans on the trail, echoed this sentiment repeatedly on the Sunday talk shows.

"That's their decision," Ohio Gov. John Kasich said on NBC's "Meet the Press," of Senate Republicans' position, allowing that the president has his prerogatives. "The Senate has a prerogative, too," he added.

New Hampshire Sen. Kelly Ayotte, a Republican facing a tough re-election bid this fall, added her voice to the chorus later Sunday. “We’re in the midst of a consequential presidential election year, and Americans deserve an opportunity to weigh in given the significant implications this nomination could have for the Supreme Court and our country for decades to come."

Senate Democrats were having none of it.

"Article II Section 2 of the Constitution says the President of the United States nominates justices to the Supreme Court, with the advice and consent of the Senate," Sen. Elizabeth Warren, D-Mass., said in a statement released on Sunday. "I can't find a clause that says '...except when there's a year left in the term of a Democratic President.'"

So while McConnell might want to move forward on any number of issues, whether spending bills or the annual Defense Department authorization bill or anything else, it's worth noting the Senate is governed by unanimous consent, and a single senator can slow even the most basic purposes of the chamber by simply saying, "I object."

For example, Cruz had objected to the relatively benign confirmation of U.S. ambassadors to Sweden and Norway until last week, when a pre-recess agreement allowed for their confirmations by unanimous consent.

Cruz didn't even have to be present to object, relying on other senators, including McConnell, to object to Democrats' attempts to move them along.

Sen. Amy Klobuchar, D-Minn., came to the floor multiple times over the course of the past few weeks to push for consent for the ambassadorial nominees and her attempts were blocked before Friday, when McConnell asked for, and was granted, unanimous consent to clear those and other nominations that had built up.

No one objected, so the nominees were confirmed. But no senator is under any obligation not to gum up the works if he or she feels the need.

Senate Democrats were already smarting over the pace of confirming nominees to the district and circuit courts . Republicans, including Cruz and Rubio on the Sunday shows, have cited the so-called "Thurmond Rule" in saying the chamber shouldn't confirm any such nominees in the last year of a president's term once the presidential race is underway. It's named after Sen. Strom Thurmond, R-S.C., who chaired the Judiciary Committee from 1981 to 1987.

"There is no such thing as the Thurmond Rule," Senate Judiciary ranking member Patrick J. Leahy, D-Vt., said on CNN's State of the Union on Sunday. Leahy cited the Democratic-controlled Senate's confirmation of several of Republican George W. Bush's lower court nominees in September 2008 as evidence that there is no such tradition or rule.

Leahy said a delay in filling a Supreme Court vacancy -- for as long as a year -- could have political repercussions for the GOP.

"I think that will guarantee they lose the Senate," he predicted. Some of the most highly contested Senate races where Republicans are running for re-election are either in Democratic states such as Illinois (Mark S. Kirk) or perennial swing states: Pennsylvania (Patrick J. Toomey), Wisconsin (Ron Johnson) and New Hampshire (Kelly Ayotte.)

But Republicans, facing a restive base in an election year, might feel they have no choice, regardless of the consequences for the legislative agenda or such electoral risk.

"They have to block this nomination," conservative radio host Hugh Hewitt said on CNN.